Burnley have so far fulfilled only one home game in the league this season with matches against Wigan, Everton and Sunderland also waterlogged or frozen off.
Accrington Stanley chief executive Rob Heys told the Lancashire Telegraph: "We are sympathetic to the problems we have had with our pitch this year.
"We've had problems with our own home games as well as the other games we've tried to get on. We tried to do something about it at Christmas but it was only a temporary solution until the end of the season.
"We've never had so many first team games called off, but there's not a lot we can do about it until the summer."
He added: "I apologise for the inconvenience caused to Burnley and their supporters and will look in to what's gone on."
Burnley Supporters Club chairman Barrie Oliver said: "It's time we played them back at Turf Moor, or found an alternative venue.
"It must be getting frustrating for the players, management and everyone. To have played one home reserve game halfway through the season is a joke."